Related papers: Euler Systems and Selmer Bounds for GU(2,1)

Kings, Lei, Loeffler and Zerbes constructed a three-variable Euler system $\kappa({\bf g},{\bf h})$ of Beilinson-Flach elements associated to a pair of Hida families $({\bf g},{\bf h})$ and exploited it to obtain applications to the…

We construct an Euler system for Galois representations associated to cohomological cuspidal automorphic representations of the group GSp(4), using the pushforwards of Eisenstein classes for GL(2) x GL(2).

This paper is about the Iwasawa theory of elliptic curves over the cyclotomic $\mathbb{Z}_p$-extension $\mathbb{Q}^{\text{cyc}}$ of $\mathbb{Q}$. We discuss a deep conjecture of Greenberg that if $E/\mathbb{Q}$ is an elliptic curve with…

In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin Galois representations corresponding to automorphic forms…

To apply the Euler system method to a $p$-adic Galois representation $T$, one needs the existence of a $\sigma \in G_{\mathbb{Q}(\mu_{p^{\infty}})}$ such that $V/(\sigma-1)V$ is free of rank one over the coefficient ring: we say that such a…

Let $E_{/\mathbb{Q}}$ be an elliptic curve and $p$ be an odd prime number at which $E$ has good ordinary reduction. Let $Sel_{p^\infty}(\mathbb{Q}_\infty, E)$ denote the $p$-primary Selmer group of $E$ considered over the cyclotomic…

We compare the Pontryagin duals of fine Selmer groups of two congruent $p$-adic Galois representations over admissible pro-$p$, $p$-adic Lie extensions $K_\infty$ of number fields $K$. We prove that in several natural settings the…

We prove the Bloch--Kato conjecture for certain critical values of degree 8 $L$-functions associated to cusp forms on $\mathrm{GSp}_4 \times \mathrm{GL}_2$. We also construct a $p$-adic Eichler--Shimura isomorphism in Hida families for…

We investigate Eisenstein congruences between the so-called Euler systems of Garrett--Rankin--Selberg type. This includes the cohomology classes of Beilinson--Kato, Beilinson--Flach and diagonal cycles. The proofs crucially rely on…

The aim of this paper is to prove inequalities towards instances of the Bloch-Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the $L$-function at the central point is zero or one. We achieve…

We construct a new Euler system (anticyclotomic, in the sense of Jetchev-Nekovar-Skinner) for the Galois representation $V_{f,\chi}$ attached to a newform $f$ of weight $k\geq 2$ twisted by an anticyclotomic Hecke character $\chi$ defined…

In the present paper, we study the $p$-adic $L$-functions and the (strict) Selmer groups over $\mathbb{Q}_{\infty}$, the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$, of the $p$-adic weight one cusp forms $f$, obtained via the…

Let $\Pi$ be a cuspidal automorphic representation of $\mathrm{GL}_{2n}(\mathbb{A_Q})$ and let $p$ be an odd prime at which $\Pi$ is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded $p$-adic…

Let $A$ be an abelian variety over a global function field $K$ of characteristic $p$. We study the $\mu$-invariant appearing in the Iwasawa theory of $A$ over the unramified $\mathbb{Z}_p$-extension of $K$. Ulmer suggests that this…

In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are associated to $p$-adic representations over number fields. We now…

We use the theory of reduced determinant functors from [24] to give a new, computationally useful, description of the relative $K_0$-groups of orders in finite dimensional separable algebras that need not be commutative. By combining this…

Let $p\geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$-torsion in the Bloch-Kato Selmer group can be made arbitrarily large. Our result extends…

Let p be an odd prime and let E be an elliptic curve defined over a quadratic imaginary field where p splits completely. Suppose E has supersingular reduction at primes above p. We define and study the fine double-signed residual Selmer…

In this paper, we relate three objects. The first is a particular value of a cup product in the cohomology of the Galois group of the maximal unramified outside p extension of a cyclotomic field containing the pth roots of unity. The second…

We show that the suspended pinch point can be seen as an elliptically fibered variety with singular fibers of type I$_2$ over codimension-one points of the base and a torsionless Mordell--Weil group of rank one. In the F-theory algorithm,…